An order-of-magnitude analysis is applied to the Navier-Stokes equations and the continuity equation for isothermal, radial fluid flow between oscillating and rotating disks. This analysis investigates the four basic cases of 1) steady, radial flow, 2) unsteady, radial flow, 3) steady, spiral flow, and 4) unsteady, spiral flow. It is shown that certain values of particular dimensionless parameters for general cases will reduce the Navier-Stokes equations to simplified forms and thus render them amenable to closed-form solutions for, say, the pressure distribution between oscillating, rotating disks. The analysis holds for laminar and turbulent flows and compressible and incompressible flows. The conditions that must be satisfied for one to reasonably neglect 1) rotation, 2) unsteady terms, and 3) convective terms are set forth. One result shown is that only rarely could one reasonably neglect the radial convective acceleration while retaining the radial local acceleration.
Fluid-Inertia Effects in Radial Flow Between Oscillating, Rotating Parallel Disks
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Warinner, D. K., and Pearson, J. T. (January 1, 1981). "Fluid-Inertia Effects in Radial Flow Between Oscillating, Rotating Parallel Disks." ASME. J. of Lubrication Tech. January 1981; 103(1): 144–149. https://doi.org/10.1115/1.3251603
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